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and A3 = 125, then find a 3 What is the value of a11A11+ a12A12+ a13A13 with respect to determinant A of order 3 4 A and B are square matrix of order 3 

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**A matrix can be named using its dimensions Dimension Matrices 4 Determinants Determinant of a 2x2 matrix: Find the determinant of each: 1 5 7 11 8 2

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4 2 −1 −4 3 7 −32 30 −42 Step 3: Add the downward numbers together – 32 + 30 + (–42) = –44 Step 4: Add the upward numbers together –72 + 140 + 

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These worksheets cover four operations, determinants, matrix equations, linead systems Array multiplication worksheets This Algebra 2 matrix worksheet will create diagnostico de anemia gestacional pdf , y por eso rompimos 2 pdf google 

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Worksheet by Kuta Software LLC Kuta Software - Infinite Date________________ Determinants of 2×2 Matrices Evaluate the determinant of each matrix 1)

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Notes on Matrices 4-1-2 Definition of a Matrix Element **A matrix can be named using its dimensions. Dimension Examples: 1. A =2!1

05 !48

2. B =1

2 3 4

3. C =053!1

!2096

Row Matrix Column Matrix Square Matrix Using matrices to solve problems: Jim, Mario and Mike are married to Shana, Kelly and Lisa. Mario is Kelly's brother and lives in Florida with his wife. Mike is shorter than Lisa's husband. Mike works at a bank. Shana and her husband live in Kentucky. Kelly and her husband work in a candy store. Who is married to whom? Find out using a matrix!

Matrices 2 Equal Matrices Solve for x and y. 1. 2x 2x+3y y 12

2. 3x+y

x!2y x+3 y!2

3. 2x33z

=53y9

Adding and Subtracting Matrices Only matrices with ______________________________ can be added or subtracted. The resulting matrix has ___________________ dimensions. Examples 1. !204

3!1012

3!2!2 !460 !152!4 671

2. 3!4

02 468
024

3. 2!18

20!5 !42 !51

4. !3102

!108!6 010 543
210
!8!10!4 Matrices 3 Scalar Multiplication Examples: 1. !27!10 2. 4 !20 4!5 3. !5 12!3 4!56 !78!9

Matrix Multiplication **Multiply rows times columns** **You can only multiply if the number of columns in the 1st matrix is equal to the number of rows in the 2nd matrix. 1. 21392

34576

2. 39221

57634

3. 1211

1327
2618
x y z

4. 0143

1025
Matrices 4 Determinants Determinant of a 2x2 matrix: Find the determinant of each: 1. !5!7 118
2. 32 !15

3. 10!2

0!3

**To find a determinant you must have a _________ matrix!! Determinant for a 3x3 matrix: Expansion by minors *minor of an element is the determinant formed when the row and the column containing that element are deleted! Examples: 1. !238

67!1
!459

2. 5!12

2!35 32!3

3. !104

2!22 30!1
Matrices 5 Determinant for a 3x3 matrix: Diagonal Method Examples: 1. !238 67!1
!459

2. 5!12

2!35 32!3

3. !104

2!22 30!1
Solving Systems using Cramer's Rule Cramer's Rule:

Matrices 6 Identity and Inverse Matrices Identity Matrix Inverse of a 2x2 matrix Examples: 1. 53

21
2. 12 34

3. 2!5

07 ???Is there ever a square matrix that does not have an inverse???

Matrices 7 Solving Systems of equations using matrices • Coefficient Matrix • Variable Matrix • Constant Matrix Example: 3!2

41
x y 7 8 Steps to solving: 1. 2. 3. Example: Solve using the inverse matrix method 4x!12y=7 x+6y=9quotesdbs_dbs19.pdfusesText_25